A theoretical investigation of the effect of Ga alloying on thermodynamic stability, electronic-structure, and oxidation resistance of Ti2AlC MAX phase

We present a systematic investigation of thermodynamic stability, phase-reaction, and chemical activity of Al containing disordered Ti2(Al-Ga)C MAX phases using machine-learning driven high-throughput framework to understand the oxidation resistance behavior with increasing temperature and exposure to static oxygen. The A-site (at Al) disordering in Ti2AlC MAX (M=Ti, A=Al, X=C) with Ga shows significant change in the chemical activity of Al with increasing temperature and exposure to static oxygen, which is expected to enable surface segregation of Al, thereby, the formation of Al2O3 and improved oxidation resistance. We performed in-depth convex hull analysis of ternary Ti–Al–C, Ti–Ga–C, and Ti–Al–Ga–C based MAX phase, and provide detailed contribution arising from electronic, chemical and vibrational entropies. The thermodynamic analysis shows change in the Gibbs formation enthalpy (ΔGform) at higher temperatures, which implies an interplay of temperature-dependent enthalpy and entropic contributions in oxidation resistance Ga doped Ti2AlC MAX phases. A detailed electronic structure and chemical bonding analysis using crystal orbital Hamilton population method reveal the origin of change in phases stability and in oxidation resistance in disorder Ti2(Al1−xGax)C MAX phases. Our electronic structure analysis correlate well with the change in oxidation resistance of Ga doped MAX phases. We believe our study provides a useful guideline to understand to role of alloying on electronic, thermodynamic, and oxidation related mechanisms of bulk MAX phases, which can work as a precursor to understand oxidation behavior of two-dimensional MAX phases, i.e., MXenes (transition metal carbides, carbonitrides and nitrides).


Scientific Reports
| (2022) 12:13090 | https://doi.org/10.1038/s41598-022-17365-y www.nature.com/scientificreports/ Ti 2 AlC based MAX phases are projected as potential candidates for fuel coating and structural applications in nuclear (fusion and fission) reactors for their superior oxidation resistance properties [14][15][16][17] . Recently however, Sokol et al. has reported that Ti 2 AlC does not provide a suitable protective coating against oxidation, while Cr 2 AlC was found to produce a suitable oxidation barrier, i.e., an outstanding candidate 18 . Notably, the Ti 2 GaC is another candidate material with remarkable electronic (phase stability and electronic-structure), structural (stability of crystal phases), and mechanical (exceptional thermal shock resistance and damage tolerance, excellent oxidation resistance, and elastic stiffness) properties 1,[19][20][21][22][23][24][25][26][27] . Several ab-initio calculated MAX phase properties were found in good agreement with experiments [28][29][30][31][32] , although high temperature studies of oxidation behavior of disordered Ti 2 AlC/Ti 2 GaC MAX phase are limited 33 . Therefore, it remains a challenge to understand the role of disorder and temperature on thermodynamic and oxidation resistance properties with respect to increasing exposure to oxygen. Furthermore, the chemical-disorder can significantly change the thermodynamic and oxidation behavior of MAX phases, altering the electronic structure properties of MAX phase. This suggests a strong connection of chemical disorder with electronic and thermodynamic properties [34][35][36][37] .
In this work, we performed a detailed electronic-structure and thermodynamic analysis of Ti 2 AlC MAX phases with a A(Al/Ga)-site disorder to provide mechanisms controlling oxidation behavior. To understand the overall oxidation process, we used a high-throughput framework comprised of a machine learning model and the grand-canonical linear programming (GCLP) method and analyzed the temperature-dependence of Gibbs formation enthalpy (∆G form ) of Ti 2 (Al 1−x Ga x )C MAX phases. An in-depth thermodynamic analysis using convex hull of ternary Ti-Al-C, Ti-Ga-C, and Ti-Al-Ga-C based MAX phase was performed to provide detailed contribution arising from electronic, chemical and vibrational entropies. Our model is able to predict reaction products, phase-fractions, and chemical activities during the high-temperature reaction processes at given temperature and oxygen content. In general, the oxidation process can be attributed to the atomic interactions that arise from varying electronic states of different species that may enable or disable the formation of different kinds of oxides. Therefore, we systematically investigated the electronic-structures of series of Ga-doped Ti 2 AlC MAX phases using ab initio methods to reveal the quantum mechanical origin of change in elemental chemical activity from alloying. To prove the charge effect on stability, we also performed chemical bonding analysis using crystal orbital Hamilton population (COHP) method. We believe that our study will guide experimentalists in understanding temperature dependent oxidation reaction processes in disorder MAX phases, exemplified for Ti 2 (Al 1−x Ga x )C MAX, which can be used to understand more complex MAX phases or even 2D MXenes.

Methods
Electronic-structure calculation. The electronic-structure calculation was performed using densityfunctional theory method as implemented within Vienna Ab initio Simulation Package [38][39][40] . The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional 41 was employed for geometrical and electronic relaxations of Ti 2 (Ga x Al 1−x )C MAX with total energy and force convergence criteria of 10 -6 eV and 0.01 eV/Å. The Brillouin zone integration in ionic and charge self-consistency were performed on 6 × 6 × 2 and 12 × 12 × 4 k-mesh using Monkhorst-Pack method 42 with a plane-wave cutoff energy of 520 eV, where the effect of the core electrons and interaction between the nuclei and the valence was treated by the projector-augmented wave (PAW) 43,44 . Based on the work of Söderling et al. 45 and Giese et al. 46 , we chose PBE was chosen over LDA or meta-GGA 47,48 exchange-correlation functionals, where it was shown that PBE provides accurate bonding properties, magnetic moments, and energetics comparing LDA or meta-GGA. The 128 atom random supercell with disorder at Al site (x = 0.25, 0.50, 0.75) in Ti 2 (Ga x Al 1-x )C MAX to avoid effect arising from cell size 49 .
High-throughput machine-learning (SISSO) framework for oxidation analysis. The machine-learning-based high-throughput method was used for assessing ∆G form , phase-prediction, and chemical activity analysis of constituent elements of Ti 2 (Ga x Al 1−x )C MAX phase. The SISSO (Sure Independence Screening and Sparsifying Operator) trained machine-learning model 50 was integrated with grand-canonical linear programming (GCLP) method 51 into a single high-throughput framework 52,53 . The SISSO model uses DFT based formation enthalpy ( �H form ) database to predict temperature dependent , and x are vibrational (phonon) entropy, elemental energies, and the stoichiometric weight of each element in the compound, respectively. The ∆G form also uses DFT-calculated ground state properties, including enthalpies of formation ( H form ) and volume. The H form of Ti-Al/Ga-C MAX phase was calculated as E is the total energy of the alloy, n i is the number of atoms and E i elemental energy of atom of type 'i' . The �G SISSO (T) is estimated from machine learning trained Bartel model 56 : where V is the volume calculated from the DFT and T is the temperature. The stable Ti-O, Al-O and Ga-O oxide phases were taken from NIST-JANAF database (experiments) for validation 54,57 . Grand canonical linear programming (GCLP). The GCLP method was used to minimize the free energy of the mixture to identify equilibrium alloy phases: where the G P is the free-energy of competing crystalline phases, and f P is the phase-fraction. The G expression was used to minimize the free energy and predict favorable phases from Ti-Al-Ga-C + O 2 reactions.

Results and discussion
Convex hull analysis for Ti 2 AlC and Ti 2 GaC. We constructed the ternary Ti-Al-C and Ti-Ga-C convex hull based on experimentally stable and theoretically known 56 unstable phases in Fig. 1a,b. Notably, the coexistence of different phases occurs when a point lies on the simplex of the hull. The stable (green) and unstable (red) MAX phases including Ti 2 XC, Ti 5 X 2 C 3 , Ti 3 XC 2 , and Ti 4 XC 3 are also marked the energies, and ΔG form at 300 K, 1000 K, 1500 K are listed in Table 1. Other unary, binary, and ternary phases are marked. The stable phases lie on the connecting lines within convex hull formed between compounds and their elemental reference states 58,59 . The focus of our study is on the Ti 2 XC MAX phases with 2:1:1 stoichiometry, interestingly, both Ti-Al-C (#1, Fig. 1a) and Ti-Ga-C (#1, Fig. 1b) has only 2:1:1 as common stable MAX phase.
Phase stability analysis of Ti 2 (Al 1−x Ga x )C MAX phase. The Fig. 2a shows the formation energy (E form ) of Ti 2 (Al 1−x Ga x )C calculated with the density-functional theory framework. Clearly, the increase in Ga at.% enhances the stability of Ti 2 (Al 1−x Ga x )C with respect to pure Ti 2 AlC MAX phase. In Fig. 2b, we show the temperature dependent Gibbs formation enthalpy (ΔG form ) of Ti 2 (Al 1−x Ga x )C from 300 to 2000 K. At room temperature (RT), Ti 2 (Al 1−x Ga x )C shows decrease in phase stability with increasing Al, where a crossover for Al cases at 800 K (x (Al) = 0, 0.25, 0.50, and 0.75 at.-frac.), energies are listed in Table 1. The ΔG form shows weakly separated stability regions with respect to temperature at 800 K, i.e., below 800 K and over 800 K. The change in the ΔG form at higher temperatures implies an interplay of temperature-dependent enthalpy and entropic contributions. This highlights the importance of temperature effect on ΔG form , which is an important quantity that allows efficient determination of the most stable equilibrium state and can thus be used to assess the resulting reaction products for a given set of reactants 52 . Figure 3 shows the formation energy difference (ΔE form ) of Ti 2 (Al 1−x Ga x )C were calculated within DFT method while temperature dependence was calculated ML framework 52 . The G f orm in Fig. 3 is plotted with respect to Ti 2 GaC (x = 0) and Ti 2 AlC (x = 1) MAX. Clearly, the increase in Ga at.% enhances the stability of Ti 2 (Al 1−x Ga x ) C, and the conclave slope in G f orm further confirms the mixing of Al-Ga on A-site. However, the G f orm with respect to end points (Ti 2 GaC and Ti 2 AlC) in Fig. 3 is very small at 300 K, i.e., increase in relative stability on Al doping does not change drastically. While increasing energy difference at higher temperatures (1000 K, 1500 K)   Fig. 4 is the outcome of Gibb's enthalpy analysis at a given temperature, which uses enthalpy of formation of different phases taking part in   Table 1) with respect to Ti 2 GaC (x = 0) and Ti 2 AlC (x = 1). Table 2. The formation enthalpy and entropy contributions for Ti 2 (Al 1−x Ga x )C MAX phases. The electronic entropy was calculated from DFT [38][39][40] , the chemical entropy was estimated with relation 1/4(2 × 0 + 1 × ( i c i lnc i ) + 1 × 0), and vibrational contribution to entropy was predicted from Bartel Model 56 as implemented in our framework 52 . The volume and energy are in Å 3 -atom −1 and eV-atom −1 , respectively. O) disappear at 1500 K, which is in agreement with the phases reported in high-temperature thermochemical NIST-JANAF dataset 54 . Some of the phases of Ti x O 1−x that undergo a phase change at higher temperatures are ignored 56 . The TiO 2 , Al 2 O 3 and Ga 2 O 3 oxide phases that considered key for oxidation resistance remain most stable oxide phases, which may play a key role during oxidation process in disorder Ti 2 (Al 1−x Ga x )C MAX phase. This is not straightforward conclusion as changing chemistries can have unexpected effects on phase formation and stability; therefore, it would be interesting to see how oxidizing environment impacts our final products and material survivability.

Oxidation analysis of Ti 2 (Al 1−x Ga x )C MAX phases.
(i) x (Al) = 0.0 and 1.0 In Fig. 5a,b, we analyze the oxidation behavior of Ti 2 AlC/Ti 2 GaC and show the heat map of the molar phase-fractions of reaction products (the color bar on right represents the molar percent, or phase fraction, of each phase). In Fig. 5a, the heatmap shows the presence of Al 2 O 3 at all temperatures    Fig. 5a,b, the TiO forms first, which followed by the reaction of oxygen with higher order MAX phases gradually transforms to TiC. At high oxygen contents, the MAX phase eventually disintegrates completely into solid Al 2 O 3 , TiO 2 , and gaseous CO 2 phase, which is in agreement with our oxide phase discussion in Figs. 3 and 4.
To understand the reaction mechanism arising changing chemical potential on varying molar oxygen percent, which represents the exposure time of the alloy to static air in experimental conditions. The reaction products of the chemical process during the selective oxidation of Al/Ga or Ti in Ti 2 AlC/Ti 2 GaC can be written as:  Fig. 6a,b. The (partial) chemical potential of (Ti, Al/Ga, C, O) is calculated for an open system using unknown molar concentration of reaction products by mixing of grand-canonical ∆G form from 300 to 2000 K. The reaction chain is associated with the reductions in the partial chemical potentials of Ti and Al, but an increase in the chemical potential of O with increasing oxygen content while C remains almost unchanged except at high oxygen content and high temperature. The higher Ti/Al activity at the early oxidation stage is directly related to their partial chemical potentials. Two chemical potentials zones in Fig. 6a,b with increasing oxygen content are identified-(a) slowly varying (0-20 mol oxygen); and (b) sharp changing (> 20 mol oxygen). The sharp change in chemical potential occurs in the region > 10 mol oxygen as Ti 3 AlC 2 , Ti 3 GaC 2 , Ti 4 GaC 3 , Ti 3 AlC 2 , TiC completely disintegrates by then, moreover, C oxidizes to form gaseous CO 2 . The occurrence of C and CO 2 at higher temperature suggests loss of carbon. The predicted trend in chemical potential suggests increased oxygen activity at higher oxygen content. It is obvious from Fig. 6a,b that Al activity is higher than Ga in MAX phase. This also could be correlated to Ellingham diagrams, where Al 2 O 3 has much lower partial pressure compared to Ga 2 O 3 .

Elemental chemical potentials.
Our framework treats all elemental reservoirs as an ideal gas model.
The resulting phases at a particular temperature are determined by those that result in a minimal energy of the system. At any temperature the amount of oxygen is incrementally increased over a range of values, i.e., a variable oxygen reservoir. As more oxygen becomes available, greater oxygen dense phases are predicted to form Ti 2 O over TiO 2 . From a particular profile, we can solve for the individual chemical potentials using the GCLP model via relation μ i = ∂U/∂N , where μ i is the chemical potential of `i' element. The chemical potential of an oxygen gas molecule changes with temperature and partial pressure, however, we considered partial pressure of 1 atm in all our calculations assuming experimental conditions with normal pressure. The accepted energy of oxygen gas phase was calculated from DFT at (0 K), which is − 9.67 eV per atom, and listed in the OQMD dataset in the same manner as other unary components. The nominal change in oxygen ratio during oxidation reaction at each temperature changes the chemical potential when we solve grand canonical linear programming (GCLP) method. The temperature dependence of the chemical potential of oxygen is considered from the thermo-chemical tables 54 .
(1)     Figs. 7, 8 and 9b. The (partial) chemical potential of (Ti, Al/Ga, C, O) is shown from 300 to 2000 K and is calculated by the mixing of ∆G form using GCLP. Similar to Ti 2 AlC, the reaction chain associated with the reductions in the partial chemical potentials of Ti and Al is shown. The chemical potential of Ga slightly increases then decreases, possibly due to the appearance of metastable oxide phase GaO, which disappears at higher temperature and high oxygen content. The increase in the O chemical potential with increasing oxygen content while C remains almost unchanged or weakly changed except at high oxygen content and high temperature. The higher Ti/Al activity compared to Ga at the early oxidation stage is directly related to their partial elemental chemical potentials. Two chemical potentials zones in Figs. 7, 8 and 9b with increasing oxygen content are identified-(a) slowly varying (0-10 mol oxygen); and (b) sharp changing (> 10 mol oxygen). The sharp change in chemical potential occurs in the region > 10 mol oxygen as Ti 2 AlC 2 /Ti 3 AlC 2 /TiC completely disintegrates by then, moreover, C oxidizes to form gaseous CO 2 . The occurrence of C and CO 2 at higher temperature suggests loss of carbon. The predicted trend in chemical potential suggests increased oxygen activity at higher oxygen content. Similarly, for Ga doped cases, we observed that chemical activity of Al increased in the intermediate and higher exposure to oxygen at all temperatures compared to pure Ti 2 AlC in Fig. 6. This suggests that Ga can be used as a catalyst in Al based MAX phases to control the elemental chemical activity.

Discussion
The Al 2 O 3 was seen at all temperatures and all oxygen concentrations due to the high chemical activity of Al, see Figs. 5, 7, 8 and 9a, as well as the very exothermic nature of the Al 2 O 3 phase itself. The weak metallic bonding between Ti-Al (2.84 Å) compared to Ti-Ga (2.79 Å) also contribute to the increased Al diffusivity 60 , which results into later appearance of Ga-based phases at low temperature and low oxygen content. The formation of Al 2 O 3 results into Al/Ga depletion in Ti 2 (Al 1−x Ga x )C at the early-stage oxidation. This in turn leads to the decomposition of the MAX phases into TiO, Al 2 O 3 , and Ti 2 AlC/Ti 2 GaC, Ti 3 AlC 2 and Ti 4 GaC 3 at low oxygen concentration. This indicates that Ti and Al/Ga are the first oxidizing elements when Ti 2 (Al 1−x Ga x )C in Figs. 7, 8 and 9 was exposed to ambient air at elevated temperatures. On further increasing the oxygen concentrations, the Al 2 O 3 oxide scale remains stable compared to other oxides as partial pressure to form Al 2 O 3 is much lower than of TiO 2 61 or Ga based phases 62 . The weaker binding of Al with C or Ti 63,64 in Ti 2 (Al 1−x Ga x )C compared to Ga and better Al diffusion 60 eases the Al 2 O 3 growth. The better thermodynamic stability of Al 2 O 3 compared to other phases during oxidation of Ti-Al-Ga-C also helps in stabilizing Al 2 O 3 at elevated temperatures. The C and CO 2 appear as the reaction products at higher temperature, which suggests C loss and the evaporation of CO 2 from the oxide scale 62 . The reaction product of in Ti 2 (Al 1−x Ga x )C oxidation reaction correctly reproduces experimentally observed phase-fractions. We also found that Al 2 O 3 forms at all temperature and all oxygen contents but Al 2 O 3 stops forming at very high-T and high-O 2 due to higher stability of spinel phase oxides. The appearance of a more stable spinel oxide phase hampers the Al 2 O 3 formation, which is the reason Al 2 O 3 is not observed at high-T. For clarity, however, the Al 2 O 3 formed at the early oxidation stage will remain in the system and work as a protective layer. Notably, the spinal phase becomes more favorable both due to its favorable thermodynamics and requirement of low Al content.
Electronic-structure of Ti 2 (Al 1−x Ga x )CMAX. As discussed in the oxidation section, the chemical activity of Al has increased as the Ga reduces the interaction with M-A layer. The question arises that what changes in the electronic structure correlates with the oxidation behavior in the MAX phase. The detailed electronic nature of Ti 2 (Al 1−x Ga x )C was analyzed using electronic density of states (DOS) and charge-density difference in Figs. 10 and 11, respectively.
The DOS is an effective tool to reveal the hybridization among the different electronic states. In Fig. 10a-d, we plot total and partial DOS to understand the effect of Ga alloying, where the Fermi level (E Fermi ) is set at zero. Our goal is to understand to role of electronic structure on oxidation behavior of Ti 2 (Al 1-x Ga x )C MAX. The Ga doping in Fig. 10a shows strong change Ti-3d and Ga-4p states near − 4 eV and − 1 eV as shown in two highlighted zones. Clearly, the DOS in Ga doped cases is significantly reduced compared to parent phase, i.e., Ti 2 AlC MAX. The prime contribution at the E F in the DOS comes from the Ti-3d ([Ar]3d 2 4s 2 ) states as shown in Fig. 10b-d, while Ga-4p ([Ar]4s 2 4p 1 ) and Al-3p ([Ne]3s 2 3p 1 ) also contribute but lesser in magnitude compared to the Ti-3d. The valence states could be divided into three energy range, i.e., (i) − 12.0 eV to − 9.0 eV, (ii) − 9.0 eV to − 2.0 eV, and (iii) − 2.0 to 0.0. The DOS at the lower energies in the region (i) show peaks at nearly − 10 eV is mainly comprised of Ti-3d and C-2 s below the E F (not shown in the Fig. 10 as they are not chemically activity), which gives rise to the formation of stronger Ti-C bonds. While energy states for Ga doped cases in the region (ii) comprised of Ti-3d, Al-3p, and Ga-4p in Fig. 10b-d. Notably, in the region (iii), we found an increased Ga-4p states near the E F , which shows strong overlap with Ti-3d bands.
The DOS in both parent and Ga-doped phases are mainly contributed by the Ti-3d 2 , C-2p 1 , and Al-3p 1 states. The Ti-3d and Ga-4p/Al-3p hybridized strongly that lead the peaks in the low energy region of both total and (8) Ti 2 (Al 0.75 Ga 0.25 )C + 2y · O 2 → 2Ti 2−2x (Al 0.75 Ga 0.25 )C + 2y · TiO 2 + TiAl 2 O 5 + TiGa 2 O 5 .  Fig. 10 are the consequence of the hybridization between different orbitals that defines the energy of the hybridized states. The peak positions show weak shift both in the valence and the conduction bands, which is expected to have no major effects on electronic structure. Meanwhile, the partial DOS analysis in Fig. 10b-d, shows changes in hybridization between Ti and C when Al is doped with Ga, while the MAX phase remains thermodynamically stable in the hexagonal phase. This change in energy of bonding states due to Ga-doping reflects the change in the Ti-C hybridization strength, consequently, the bonding strength between unlike atoms. The finite DOS at the E F indicates that doped Ga atoms could not change the metallic character. At the top of the valence band, an interaction between Ti-3d and C-2p peaks in the energy range of − 2.0 eV and − 5 eV that leads to strong hybridization, and results into a strong directional bonding. A peak or a valley like structure in DOS at E F signifies the presence of a pseudo gap, which is a signature of both chemical and structural stability 59,[65][66][67] . The presence of pseudo-gap region and alloys stability has its origin in several active electronic mechanisms including charge transfer and change in hybridization that pulls down the electronic DOS from E F either below the Fermi level or above it 67,68 . In Fig. 10, we found that the decreases electronic density of states at E F originates from change in mixing of the Ti-3d states with Al-3p due to Ga alloying, which shows increase in Ga-4p states near − 1 eV with increasing at.% Ga. This correlates well with the   Table 1). The A-site alloying weakens the bonding in Ti-Al-Ga-C MAX. This suggests that Ga can be tuned to manipulate chemical activity of Al based MAX.
The charge density analysis: The direction of intra-layer (Ti-C/Al-Ga) and inter-layer (Al/Ga-C) charge transfer is also an important feature of MAX phase stability. In Fig. 11a,b, we plot the charge density difference ( �ρ = ρ Ti2(Al1−Gax)C − ρ Ti2AlC ) for Ti 2 (Al 1− Ga x )C for x = 1.0, and 0.50, where blue color represents the charge from the Ti 2 AlC MAX while the yellow color is charge readjustment. Our charge plot in Fig. 11 shows no effective change in charge at C and Ti loses the charge. This charge asymmetry at site A-site was caused by Ga alloying in the Ti 2 AlC MAX, therefore, a varying strength of Al/Ga metallic bonds are expected. The effective charge transfer between Ga to Al shows the mechanism controlling the bonding behavior in MAX phase, which also weakens the bonding Al interaction with the Ti-C basal plane. This gain in charge density in Ti 2 GaC originates from decrease of 1.4% volume with respect to Ti 2 AlC, which is possibly one of the reasons why Al chemical activity has increased with Ga doping.
Chemical bonding analysis. We performed crystal orbital Hamilton population (COHP) analysis to elucidate the bonding behavior [69][70][71][72][73] . The COHP partitions the band structure energy into bonding, nonbonding and antibonding energy of atomic pair contribution in a specified energy range. In Fig. 12a,b, we plot-pCOHP as a function of energy for Ti 2 (Al 1−x Ga x )C, x = 0,1. Positive values of -pCOHP describe bonding energy regions whereas negative values describe antibonding energy regions. The COHP shows slightly different picture of bonding for Ti 2 GaC MAX in Fig. 12b, where Ga shows weak reduction of C-Ti bonding strength while weak increase in anti-bonding states. This indicates towards increased charge activity due to Ga as shown by charge density difference plot in Fig. 10. Notably, the antibonding states for the C-Ti appear near − 1.2 eV below the Fermi level both for Ti 2 AlC (− 1.17 eV in Fig. 12a) and Ti 2 GaC (− 1.2 eV in Fig. 12b). Both bonding and antibonding states in Ti 2 GaC show a shift below Fermi level due to charge filling, which again corroborate with our idea of increase charge activity. This is also in agreement with the fact that the Ga doping leads to lower volume and lower enthalpy as shown in Tables 1 and 2. Expectedly, Ga/Al-Ti or Ga/Al-C show antibonding (negative COHP) in the whole energy range as Al/Ga and Ti-C are in two different basal planes in MAX phase.

Conclusion
We systematically investigated the thermodynamic stability and oxidation behavior of Ti 2 AlC MAX phases with Ga alloying using high-throughput machine-learning framework combined with density-functional theory. The A-site (at Al) disordering of Ti 2 AlC with Ga shows significant change in the chemical activity of Al with increasing temperature and exposure to static oxygen. Our thermodynamic analysis shows changes in the ΔG form at higher temperatures, which implies an interplay of temperature-dependent enthalpy and entropic contributions in oxidation behavior of Ga doped Ti 2 AlC MAX phase. Therefore, we have included electronic, chemical, and vibrational entropy contribution with vibrational contribution is the largest and has significant impact on hightemperature stability of MAX phases. Our convex hull analysis of key Ti-O, Al-O, and Ga-O oxides provides validation of our framework that provides accurate phase predictions, which is critical in oxidation analysis. We also show that the increased Al activity during oxidation in Ga doped MAX phases may improve the oxide layer (Al 2 O 3 ) formation, which will serve as protection against oxygen diffusion by delaying the formation Ti-O (e.g., TiO 2 ) based phases. This also suggests that Al at.% in bulk Ti 2 (Ga x Al 1−x )C MAX is sufficient, which also indicates that improved Al activity can be significant in enhancing the protection of MAX phases against oxidation.
The phase stability analysis is an efficient determination of the most stable equilibrium state that helps to assess the resulting reaction products for a given set of reactants. We performed detailed electronic-structure, charge density, and chemical bonding (COHP) analysis to understand the change in oxidation behavior of of Ga doped Ti 2 AlC, i.e., Ti 2 (Ga x Al 1−x )C MAX. Expectedly, the COHP analysis shows that covalently bonded Ti-C shows the bonding nature in (0001) basal plane compared other pairs such as Ti-Al/Ga or C-Al/Ga, which is clearly observed by their anti-bonding behavior. The anti-bonding of Ti-Al and Ti-Ga bonds makes them easier to break, however, stronger stability of Ga doped MAX phases weakens the chemical bonding of Al with Al-Ga layer. This makes the chemical activity of Al higher compared to Ga 74 , therefore, Al atoms can diffuse easily and